Transcript Periodic Table: Why the repetition

Periodic Table: Why the repetition
•
The periodic table is the most important organizing principle in chemistry.
•
Chemical and physical properties of elements in the same group are similar.
•
All chemical and physical properties vary in a periodic manner, hence the name
periodic table.
For instance, hydrogen, lithium, sodium, and potassium, were all known to make
chlorides in a 1:1 mole ratio. The “wrapping around” of the periodic table was done to
capture these similarities into columns.
Periodic Table
Most tables in your book (other than the periodic table) look nothing like the periodic
table. Instead they are a few columns of data. The periodic table, done this way, would
look like this:
Hydrogen 1.00794
Helium
4.002602
Lithium
6.941
Beryllium
9.012181
Boron
10.811
Carbon
12.0107
Notice that the actual
periodic table does not
uniformly order the
elements by atomic mass.
(Compare argon to
potassium.)
etc.
So how did we get
the atomic
numbers?
•The
atomic masses are clearly
pretty good guides (almost
perfect, in fact)
•In 1913, an English
spectroscopist H.G.J. Moseley
performed a series of x-ray
experiments with the
following data:
Periodic Table: Predictions
Periodic Table: Microscopic Explanation
The whole rest of the chapter is generally about developing this explanation.
•The proton and the electron were the two sub-atomic particles known, so the
explanation had to involve them somehow.
•But Moseley showed the protons uniformly increase as you go along the periodic
table; they don’t behave periodically.
•So the electrons must be explanation.
•This makes sense: electrons are the outer part of the atom. Any time two atoms
meet, the electrons meet first, So they should be most important in how two atoms
interact.
Periodic Electron Behavior
Electromagnetic
Radiation
• Frequency (, Greek nu):
Number of peaks that pass a
given point per unit time.
• Wavelength (, Greek lambda):
Distance from one wave peak
to the next.
• Amplitude: Height measured from the center of the wave. The square of the
amplitude gives intensity.
Electromagnetic Spectrum
Electromagnetic Spectrum: Math
• Speed of a wave is the wavelength (in meters) multiplied by its
frequency in reciprocal seconds.
–
Wavelength x Frequency = Speed
–
 (m) x  (s–1) = c (m/s–1)
Atomic Spectra: Line spectra
•Line spectra: run the emitted light through a monochromator. very distinctive
results. Called “atomic fingerprints.”
Atomic Spectra: Hydrogen spectrum
“explained”
Balmer showed:
1
1
 R 2  2 

n 
2
1
Works for all n integers (getting weaker are n increases).
R is now called Rydberg constant.
Rydberg showed it
could be
generalized to:
1
 1
 R 2  2 

n 
m
1
For all n>m
Sadly, this equation only worked for one-electron systems like H or He+ or Li2+. Many tried to
generalize the equation for many-electron systems. All attempts failed.
The state of affairs in ~1900:
•A mathematical description of the hydrogen atom spectrum was available, but
it had no physical basis. (That is, there was no real “why”.)
•There were two kinds of “things” in the universe: particles and waves
•Particles come in discrete chunks that can be counted. That is, they are
quantized. They carry energy as kinetic energy which is infinitely adjustable.
•Waves do not come in discrete chunk but instead are continuous and thus are
not countable like particles. They are not quantized. They have wavelengths (or
frequencies) that are infinitely adjustable. They carry energy that is measurable
as the intensity of the wave. How waves carry energy is unknown.
•Phenomena yet to be explained:
•Blackbody radiation
•Photoelectric effect
•How the atom works
Blackbody radiation
When a metal chunk is resistively heated to a high enough temperature,
It starts to glow.
This glow depends only on the temperature and not on the material.
The wavelengths of light emitted decrease as the temperature increases,
starting first down in the microwave and infra-red region and sliding through
the visible from red to violet, and then into the ultraviolet.
Classically, blackbodies emit light at
the frequency they vibrate. Because
most of the atoms are highly
constrained, most should vibrate very
quickly and thus emit high frequency
light, but in truth most emit low
frequency light.
Waves as Particles:
Quantized Energy
• Blackbody radiation is the visible glow that objects with
unbound electrons emit when heated.
• Max Planck (1858–1947): proposed that energy is only emitted
in discrete packets called quanta.
• The amount of energy depends on the frequency:
E  h 
hc

h  6.626  10 34 J  s
Blackbodies explained
At the time Planck’s solution was considered a mathematical oddity. That is, he had
found an equation that had the same shape as the experimental blackbody curves, but
the explanation behind the equation was all wrong.
In fact, Planck never fully embraced quantum theory and doubted the work of Einstein
and others for the rest of his life.
But the key ideas were now out there:
light comes in discrete chunks
the energy of light is related to its frequency and not to its amplitude
the energy of these chunks of light could not be just any value
Photoelectric Effect
If you put a piece of metal in a vacuum tube, and then shine light of
certain frequency on it, the metal emits electrons. This is called the
photoelectric effect. Experimentally it was found that the light had to be
of a high enough frequency or no electrons would be emitted. And as the
light increased in frequency above this “threshhold frequency” the kinetic
energy of the electrons increased.
Classically, electrons oscillate at the frequency of the incoming light. And
the higher the amplitude of the oscillating light, the bigger the amplitude
of the electron’s oscillations. Thus any frequency of light should be able to
make a metal emit electrons, and the kinetic energy should vary only as
the intensity of the light increases.
Waves as Particles:
Quantized Energy
• Albert Einstein (1879–1955):
• Used the idea of
quanta to explain the
photoelectric effect.
• He proposed that
light behaves as a
stream of particles
called photons.
Waves as Particles:
Quantized Energy
• A photon’s energy
must exceed a
minimum threshold for
electrons to be
ejected.
• Energy of a photon
depends only on
the frequency.
Photoelectric Effect Explained
When Einstein solved his equations to fit the experimental photoelectric effect
data, he found that the photons must be carrying energy in multiples of
6.626*10-34 J s. This was exactly the constant that Planck found with entirely
different experiments!
At this point, this quantum theory of light was taken much more seriously.
While many doubters remained for decades to come, most reasoned that the
presence of the same constant (found independently) showed that there must
be something real behind the theory.
But still this does not explain the atom.
Particles as Waves:
de Broglie wavelengths
• Louis de Broglie (1892–1987): Suggested waves
can behave as particles and particles can behave
as waves. This is called wave–particle duality.
For Light
For a Particle
:  
:  
h
mc
h
mv


h
p
h
p
Rydberg and the Atom: Bohr Model
Heisenberg Uncertainty Principle
• Werner Heisenberg (1901–1976): Showed that it is impossible
to know (or measure) precisely both the position and velocity
(or the momentum) at the same time.
• The simple act of “seeing” an electron would change its energy
and therefore its position.
Heisenberg Uncertainty Principle
h
Heisenberg Uncertain ty Princip le : ( x )( mv) 
4
h
Uncertaint y in electron' s position : ( x ) 
(4 )( mv)
Electron wave functions
• Wave functions describe the behavior of electrons.
• Each wave function contains four variables called quantum
numbers. Quantum numbers must be integers. (That is, they are
quantized.) The three we need now are:
– • Principal Quantum Number (n)
– • Angular-Momentum Quantum Number (l)
– • Magnetic Quantum Number (ml)
Principal Quantum Number (n)
• Principal Quantum Number (n): Defines the size and
energy level of the orbital. n = 1, 2, 3, 
• As n increases, the electrons get farther from the
nucleus.
• As n increases, the electrons’ energy increases.
• Each value of n is called a shell.
Angular Momentum (l)
•Angular-Momentum Quantum Number (l): Defines the
three-dimensional shape of the orbital.
•For an orbital of principal quantum number n, the value
of l can have an integer value from 0 to n – 1.
•This gives the subshell notation:
l = 0 = s orbital
l = 1 = p orbital
l = 2 = d orbital
l = 3 = f orbital
l = 4 = g orbital
Magnetic Quantum Number (ml)
•Magnetic Quantum Number (ml): Defines the spatial
orientation of the orbital.
•For orbital of angular-momentum quantum number, l,
the value of ml has integer values from –l to +l.
•This gives a spatial orientation of:
l = 0 giving ml = 0
l = 1 giving ml = –1, 0, +1
l = 2 giving ml = –2, –1, 0, 1, 2, and so on…...
Quantum Numbers
Orbitals and Energy
Electron Positions
• s Orbital Shapes:
Electron Positions (II)
• p Orbital Shapes:
Electron Positions (III)
• d and f Orbital Shapes:
What are orbitals?
•Orbitals (and shells & subshells) are equations
(fundamentally).
They are four-dimensional
equations that solve the Schrodinger equation.
•They are theoretical entities.
•Two questions:
•What do orbitals represent?
•What experimental evidence do we have to
support them?
What are orbitals?
•Orbitals can be considered in two ways:
•1. Orbitals represent the “cage” in which the
electron resides. The calculated probabilities
represent the “pacing of the tiger in the cage.”
•2. Orbitals represent the electron itself. In the atom
the electron has a wave-like existence and the orbital
is the spatial area over which the wave has non-zero
amplitude. The electron has no fixed shape.
What experimental evidence?
How do atoms use shells, subshells, and orbitals?
They use shells, subshells, and orbitals to organize
electrons.
Why do atoms organize electrons?
They organize electrons in order to minimize the
energy.
So to find evidence of shells, subshells, and orbitals we
need to measure the energies of electrons in the atom.
Experimental Evidence:
Shells
Ionization Energy (IE) Experiment
X-ray (h)
eKE detector
h – KE(e-) = IE
Only capable of seeing the most easily removed electron (1IE). We can rejigger the
experiment to see 2IE, 3IE, etc.
We also cannot see how many electrons come off.
What Determines the
Electron’s Energy?
Proximity to the nucleus
The closer to the nucleus, the lower the
electron’s energy (and therefore the higher the
ionization energy of the electron.)
The greater the number of protons in the nucleus, the
greater the attraction is going to be.
What should IE vs. Z look like?
• What should IE depend on?
• As Z increases, what if the new electron is placed
randomly?
• As Z increases, what if new electron is placed in
same shell?
• As Z increases, what if each electron is placed
further away from nucleus?
• Any other possibilities to be considered?
IE Experiment Actual Data
Evidence for Subshells: PES experiments
The PES experiment works rather like the IE
experiment, but is more subtle.
It allows one to see the energy at which each
of the electrons comes off (not just the easiest
one), and how many electrons come off at
each energy.
We are still making ions.
PES Data (Hydrogen)
The most easily removed electrons from the
PES data must match the IE expt. data
The number of electrons coming off is
shown by the height of the peak
Higher ionization energies to the left, so electrons that
are further from the nucleus are to the right
PES Data (Hydrogen and Helium)
PES Data (H – Li)
Two different shells show as two peaks with a
big gap between them
PES Data (H – Be)
PES Data (H – B)
Two different shells
Two subshells in the same shell
PES Data (B – Ne)
So apparently, the way the system
works is that we completely fill a
subshell and then move on to the
next subshell, completely filling it,
until there are no more subshells
in a shell and then we move on to
the next shell.
PES Data (MJ/mol)
Element
1st peak
2nd peak
3rd peak
H
1.31 (1)
He
2.37 (2)
Li
6.26 (2)
0.52 (1)
Be
11.5 (2)
0.90 (2)
B
19.3 (2)
1.36 (2)
0.80 (1)
C
28.6 (2)
1.72 (2)
1.09 (2)
N
39.6 (2)
2.45 (2)
1.40 (3)
O
52.6 (2)
3.12 (2)
1.31 (4)
F
67.2 (2)
3.88 (2)
1.68 (5)
Ne
84.0 (2)
4.68 (2)
2.08 (6)
PES Data (Na – Sc)
Element
1st peak
2nd peak
3rd peak
4th peak
Na
104 (2)
6.84 (2)
3.67 (6)
0.50 (1)
Mg
126 (2)
9.07 (2)
5.31 (6)
0.74 (2)
Al
151 (2)
12.1 (2)
7.79 (6)
1.09 (2)
0.58 (1)
Si
178 (2)
15.1 (2)
10.3 (6)
1.46 (2)
0.79 (2)
P
208 (2)
18.7 (2)
13.5 (6)
1.95 (2)
1.01 (3)
S
239 (2)
22.7 (2)
16.5 (6)
2.05 (2)
1.00 (4)
Cl
273 (2)
26.8 (2)
20.2 (6)
2.44 (2)
1.25 (5)
Ar
309 (2)
31.5 (2)
24.1 (6)
2.82 (2)
1.52 (6)
K
347 (2)
37.1 (2)
29.1 (6)
3.93 (2)
2.38 (6)
0.42 (1)
Ca
390 (2)
42.7 (2)
34.0 (6)
4.65 (2)
2.90 (6)
0.59 (2)
Sc
433 (2)
48.5 (2)
39.2 (6)
5.44 (2)
3.24 (6)
1s
2s
2p
3s
3p
5th peak
3d? 4s?
6th peak
0.77 (1)
4s? 3d?
7th peak
0.63 (2)
Subshell Filling Order
Increasing Energy
• Filling order gets more
complicated as you get to the
later subshells
• This happens because the
electron-electron repulsion
starts to affect the energies
of the subshells pretty
substantially
Core
[He]
[Ne]
[Ar]
[Kr]
[Xe]
[Rn]
1s
2s
3s
4s
5s
6s
7s
2p
3p
4p
5p
6p
7p
We have rules!!
3d
4d 4f
5d 5f
6d
Electron Configurations
• Electron configurations label the shell and subshell of each
electron
• We use the shell and subshell labels we know from quantum
mechanics
• We use the populations we know from the PES experiments
Li: 1s2 2s1
F: 1s2 2s2 2p5
Element
1st peak
2nd peak
3rd peak
H
1.31 (1)
He
2.37 (2)
Li
6.26 (2)
0.52 (1)
Be
11.5 (2)
0.90 (2)
B
19.3 (2)
1.36 (2)
0.80 (1)
C
28.6 (2)
1.72 (2)
1.09 (2)
N
39.6 (2)
2.45 (2)
1.40 (3)
O
52.6 (2)
3.12 (2)
1.31 (4)
F
67.2 (2)
3.88 (2)
1.68 (5)
Ne
84.0 (2)
4.68 (2)
2.08 (6)
Why that particular filling order?
• Because it minimizes the energy? (But that
just changes the question.)
Zeff and Subshell Energies
Electron Shielding
• Electrons repel each other
• Electrons are attracted to the nucleus.
• Orbitals with a low ℓ have a higher intensity of
their Y near the nucleus.
• This intensity, in effect, blocks electrons
further out from feeling the full pull of the
nucleus. This is called “electron shielding.”
Effective Nuclear Charge
• Electron shielding leads to energy differences among orbitals
within a shell.
• Net nuclear charge felt by an electron is called the effective
nuclear charge (Zeff).
• Zeff = Zactual – electron shielding
Effective Nuclear Charge
• Zeff is the observed attraction to the
nucleus.
• Zeff is different for different subshells
• Zeff is lower than actual
nuclear charge.
• Zeff increases
toward nucleus
ns > np > nd > nf
• This explains certain periodic changes
observed.
Things we know
•The 1s subshell has the quantum numbers 1,0,0.
•The 1s subshell has one orbital.
•The 1s subshell holds two electrons.
•Every electron in a system needs to have different
quantum numbers.
Umm, what gives?
Electron Spin
•Electrons need to have unique quantum
number sets.
•Electrons have an additional spin quantum
number ms
•So every different orbital (1st 3 quantum
numbers) can hold two electrons, each with a
different spin quantum number.
Pauli Exclusion Principle
The Pauli Exclusion Principle states that no
two electrons (in any one atom) have the same four
quantum numbers.
Electron Configuration Principles: Aufbau
Principles
• In the atom’s most stable state, the electrons in the atom are in
the lowest energy orbital possible.
• Pauli Exclusion Principle: No two electrons in an atom can have
the same quantum numbers (n, l, ml, ms).
• Hund’s Rule: When filling orbitals in the same subshell,
maximize the number of parallel spins.
How does electron spin affect electron
energy?
•For a single electron alone in space, spin doesn’t affect the energy at all.
•Spin affects the energy of two electrons interacting with each other.
•Electrons with the same spin have slightly lower energy than
electrons with opposite spin.
•Because electrons have the same charge, putting them in different
locations (different orbitals) lowers the energy substantially.
•Together, these are the basis of Hund’s rule.
Orbital Diagrams
We now can write true electron configurations (showing
which electrons are in which orbital.)
Ironically, this is not done in orbital diagrams (rather than
in electron configurations, which we will make with only
shells and subshells labeled.) In orbital diagrams we
represent each orbital in each subshell as a box or line.
We represent each electron as an arrow pointing up or
down (representing the two different spins.)
Orbital Diagrams vs. Electron Configurations
Li
 
1s 2s
Be  
1s 2s
1s2 2s1
1s2 2s2
B
  
1s 2s
2p
1s2 2s2 2p1
C
   
1s 2s
2p
1s2 2s2 2p2
Can we see evidence for this effect?
YES!
We see it in the unexpectedly low IE of sulfur and
oxygen.
Electron Configuration Principles
• Rules of Aufbau Principle:
1. Lower n orbitals fill first.
2. Each orbital holds two electrons; each with different ms.
3. Half-fill degenerate orbitals before pairing electrons.
Writing Electron Configurations
• Configurations are written as collections of subshells.
• Start with the lowest energy orbitals and continue in
increasing energy order.
• The number of electrons in that subshell is written as
a superscript to the right of the subshell label.
• It is acceptable to abbreviate configurations by
putting the previous noble gas in brackets and
continuing from there.
Electron Configurations and the Periodic
Table
Ground State vs. Excited State
• The electron configurations we have produced
so far are all ground state configurations.
• If all the electrons are in proper orbitals
(properly), but the filling has not obeyed the
Aufbau principle, it is an excited state
configuration.
Which principles obeyed for excited states
(and ground states)?
• Only 2 electrons per orbital
• 2 electrons in an orbital must have opposite
spin
Which principles not obeyed for
excited states?
• Parallel spins unnecessary
• Filling subshells unnecessary
Anomalous Electron Configurations
•Electrons and atoms do not have attitudes. Whatever
they do they do to lower the energy of the atom.
•What lowers the energy?
•All full shells lowers the energy a LOT
•All full subshells lowers the energy somewhat
•All parallel spins lowers the energy a little, but it
increases as the number of parallel spins increases
Anomalous Electron Configurations
• Anomalous Electron Configurations: Result from unusual stability of
half-filled & full-filled subshells.
• Chromium should be [Ar] 4s2 3d4, but is [Ar] 4s1 3d5
• Copper should be [Ar] 4s2 3d9, but is [Ar] 4s1 3d10
• In the second transition series this is even more pronounced,
with Nb, Mo, Ru, Rh, Pd, and Ag having anomalous
configurations (Figure 5.20).
We’ve already seen this increased stability. Where?
Atomic
Radius
•As you move down a group the atomic size becomes bigger as new
shells of electrons become populated.
•As you move rightward across a group the atomic size generally
becomes smaller as the effective nuclear charge grows (because the
new electrons are in the same subshell as the previous electrons).